Question: Divide the following complex numbers. $ \dfrac{-12-9i}{-3i}$
Solution: Since we're dividing by a single term, we can simply divide each term in the numerator separately. $ \dfrac{-12-9i}{-3i} = \dfrac{-12}{-3i} - \dfrac{9i}{-3i}$ Factor out a $1/i$ $\dfrac{-12}{-3i} - \dfrac{9i}{-3i} = \dfrac 1i \left( \dfrac{-12}{-3} - \dfrac{9i}{-3} \right) = \dfrac 1i (4+3i)$ After simplification, $1/i$ is equal to $-i$, so we have: $\dfrac 1i (4+3i) = -i (4+3i) = -4i - 3i^2 = 3-4i$